Help with distance between cities?

[theintarnets]

Homework Statement

Find the distance in kilometers between each pair of cities assuming they lie on the same north-south line:
Panama City, Panama, 9° N and Pittsburgh, Pennsylvania 40° N

Homework Equations

All we talked about in class is that θ = S/r

The Attempt at a Solution

I'm really not sure what to do... I assume I'm supposed to be solving for s or r, given that θ1 is 9 and θ2 is 40 but...I'm still not sure what to do.

 

[PeterO]

Homework Statement

Find the distance in kilometers between each pair of cities assuming they lie on the same north-south line:
Panama City, Panama, 9° N and Pittsburgh, Pennsylvania 40° N

Homework Equations

The Attempt at a Solution

I'm really not sure what to do...

The distance between them is along an arc - if you assume the Earth is a perfect sphere - we commonly do.

 

[theintarnets]

So what am I supposed to do? All I'm given is 9 and 40. I know I need S or R, but I don't know how to get them.

 

[theintarnets]

Nevermind, I think I've got it. Apparently the radius of Earth is 6400 km. So I converted the given θ's to radians and then solved for S for the both of them, then subtracted to get the distance between the two :D Thanks for the hint, PeterO

 

[asteriatic]

Hello,

Thank you for reaching out for help with finding the distance between cities. To calculate the distance between two cities on the same north-south line, we can use the formula d = rθ, where d is the distance, r is the radius of the earth, and θ is the difference in latitude between the two cities.

In this case, we can use the latitude of Panama City (9° N) and Pittsburgh (40° N) to find the difference in latitude, which is θ = 40° - 9° = 31°. The radius of the Earth is approximately 6,371 kilometers, so we can plug in these values into the formula to find the distance between the two cities:

d = (6,371 km)(31°) = 197,401 km

Therefore, the distance between Panama City and Pittsburgh is approximately 197,401 kilometers. I hope this helps! Let me know if you have any further questions.

Best,